Intensity of Double Slit Pattern

[lha08]

Homework Statement

Could anyone help me to explain how the intensity of the double Slit pattern works because I'm looking at the formula and I'm really confused...

Homework Equations

I=4Icos^2(phi/2)
A=2Ecos(phi/2)

The Attempt at a Solution

 

[dx]

What specifically do you want explained? The formula is easy to derive geometrically using the phasor diagram. Or you can do it algebraically: since only the phase difference matters, let the complex amplitude from slit one be just A (a real number). Then the complex amplitude from slit two will be Ae^iφ. The sum is therefore A(1 + e^iφ) = A(1 + cosφ + isinφ), and the magnitude squared is A²(1 + cos²φ + 2cosφ + sin²φ) = A²(2 + 2cosφ) = 2A²(2cos²(φ/2)) = 4A²cos²(φ/2).